1. The Earth has a gravitational field that exerts a force on

objects both in and around it

Gravity and Weight on Other Planets

• Mass, Weight and Gravity

F = m.g • Weight is a measurement of the force on an object

caused by gravity trying to pull the object down. • Weight is a Vector quantity measured in Newtons.• Gravity is an attractive force. • Mass is the amount of matter contained inside an

object More Information and an activity on Weight Force

Weight

• Weight is a measurement of the force on a object caused by gravity trying to pull the object down.

• Mars has less gravity than Earth. Therefore if you were on Mars you'd weigh less because the force of gravity wouldn't be as strong as it is here on Earth.

• Does this mean you would suddenly be thinner on Mars? No. You would have the same amount of mass as you do on Earth. (Mass is the amount of stuff inside an object.)

Gravity

• Gravity is an attractive force. This doesn't mean it's pretty. What "attractive" means is that an object's gravity pulls other objects toward it.

• The Earth's gravity naturally pulls us, and everything else, toward the centre of the planet, which keeps us from drifting off into space.

• The Earth isn't the only thing that has gravity. In fact, every single object in the universe has gravity. The tables you're sitting at have gravity. They are pulling you towards them. You have gravity, and you are pulling the tables towards you. We can't see or feel these things happening because people and tables have a such a small mass that the effects of gravity cannot be seen.

Mass

• Mass is the amount of stuff contained inside an object. It takes a lot of mass to make a lot of gravity.

• The Earth has a lot of mass, so it has a lot of gravity. The moon's gravity is about 1/6 the amount of the Earth's because the moon has less mass than the Earth.

• You've probably seen video footage of astronauts walking on the moon. They seem to float between each step. Remember that the moon has about 1/6 the amount of gravity that the Earth has?

• Well, if you went to the moon, you'd weigh less than you do here on Earth. On the moon your mass would be the same -- there is no less of you on the moon. But your weight is different because the moon's gravity is different.

Calculating Gravity

• Sir Isaac Newton was the man that brought the heavens down to Earth.

• Remember Newton’s 3rd Law

“Every action has an equal and opposite reaction”• Therefore the force of gravity works in both ways. That

is, you are pulled down by gravity, but, at the same time you are pulling the earth up towards you.

• So from Newton’s work it is possible to calculate the Force of Gravity between two objects.

221

r

mmGFgravity

The Law of Universal Gravitation

221

r

mmGFgravity

Fg=Force in Newtons

G = Gravitational Constant

m1= mass of object 1 in kg

m2 = mass of object 2 in kg

r = radius or distance between the centre of the two objects.

Calculating the Force between two objects.

ProblemGiven the following data determine the magnitude of the

gravitational attraction between:a) The Earth and the Moonb) The Earth and the Sun

Mass of Earth = 5.97 x 1024kgMass of the Moon = 7.35 x 1022kgMass of the Sun = 1.99 x 1030kgAverage Earth-Moon distance = 3.84 x 108mAverage Earth-Sun distance = 1.50 x 1011mN.B. The Earth Sun Distance is also a unit of measure for space.

1 AU (Astronomical Unit) = 1.50 x 1011m2 AU therefore would be 2 x 1.50 x 1011m = 3.0 x 1011m

Answers

a) 1.98 x 1020N

b)3.52 x 1022N

So even though the Sun is further away the Force of attraction is greater than the moon.

Calculating Gravity on other Planets.

• Remember Weight is dependent upon the gravity of a planet.

• We can calculate the Gravity on a planet if we know the planet’s Mass in kg and it’s mean radius in m.

• We can use the following formula to calculate it:

planet

planetplanet r

mGGravity

Remember the Gravitational constant = 6.67x10-11 Nm2/kg2

Calculating it for Earth

• Gravity = 6.67x10-11x 5.98x1024

(6.37x106)2

= 9.83 m/s2

Now it is your turn to calculate it for each planet in our solar system.

planet

planetplanet r

mGGravity

2

Gravity on the Planets

Planet Mass(kg) Mean Radius (m)

Earth 5.98 x1024 6.37 x106

The Moon 7.36 x1022 1.74 x106

Mars 6.42 x1023 3.37 x106

Jupiter 1.90 x1027 6.99 x107

Pluto 1.4 x1022 1.5 x106

Mercury 3.18 x1023 2.43 x106

Venus 4.88 x1024 6.06 x106

Saturn 5.68 x1026 5.85 x107

Uranus 8.68 x1025 2.33 x109

Neptune 1.03 x1026 2.21 x107

Acceleration due to Gravity (m/s/s)

9.8

1.6

3.7

24.8

0.7

Your Weight on other planets

1. Estimate your mass.

2. Record your mass in the chart below. Your mass is your weight on Earth.

3. Multiply your mass times the gravity in each row to figure out your weight at each location.

4. Where do you weigh the most? Where do you weigh the least?

• To calculate your weight: mass x gravity = weight

Location Mass Gravity Weight

Earth =9.8

Earth's moon =0.17 x 9.8

Venus =0.90x9.8

Mars =0.38x9.8

Mercury =0.38x9.8

Jupiter =2.36x9.8

Saturn =0.92x9.8

Uranus =0.89x9.8

Neptune =1.13x9.8

Pluto =0.07x9.8

Let’s Investigate Acceleration due to Gravity

• First Hand Investigation

– Determine a value for gravity using pendulum motion.

Handout

Gravity and Potential Energy• When we raise something off the ground we are giving it

energy because if we drop it then it will fall to the ground.• Therefore to raise the item we have to do work to raise it off

the ground. Essentially we are working against gravity to lift the object.

• We must remember however that we are only observing gravity on the surface of the earth.

• What about when we are a long way from Earth? Does it affect us the same?

I can hardly feelgravity out here

Gee gravity feels strong hereEarth

Gravitational Fields

• We can represent the gravity around an object with field lines.

• The field lines go in towards the centre of mass.

• The field on the surface of the Earth is straight down.

• E.g. in a room

Gravity and Work

• As we have said to move something in a gravitational field we must do work or use Energy.

Therefore our idea of

PE=mgh is good but only when we are close to Earth.

How could we define it for the entire Universe?

Gravity is Inversely Proportional

• That means as an object moves away from a large object the force of gravity reduces. The faster we can go.

2

1

radiusGravity

Remember Newton’s Gravitational Force

221

r

mmGFgravity

rFW

rradiuss

sFW

r

mmGEpotential

21

rr

mmGrFW

221

Notice the negative sign, it will be explained in the next

couple of slides.

Gravitational Potential Energy and Work Done.

GPE Information from Zona Land

The gravitational potential energy of an object at some point within a gravitational field is equivalent to the work done in moving the object from an infinite distance to that point. It can be shown mathematically that the gravitational energy, Ep , of an object with mass, m1 , a distance, r , from the centre of a planet of mass, m2 , is given by:

Total Energy

• Total Energy =

Potential Energy + Kinetic Energy

Therefore drawing graphs of both Ep and Ek would look like:

Graph of Gravitational Potential Energy

r

Earth

Ep 0

+

-

d

Graph of Kinetic Energy

r

Earth

Ek 0

+

-

d

GPE

< Ep at x < Ep at Ep at suface

Now Gravity is essentially zero at infinity so at x Ep is less so it must be a negative. Hence the negative sign in the formula.

Example QuestionQuestion: A spacecraft is moved to a higher orbit. Use

the concept of energy to explain why it slows down.

Answer:

The rocket moves away from the planet, so:

Ep increases as the rocket moves further away

Ek therefore decreases

= loss of kinetic energy means rocket would slow down.

Another Problem

• Using the following data determine the Gravitational Potential Energy of:

a) The moon within the Earth’s gravitational field

b) The Earth within the Sun’s gravitational field

Mass of Earth = 5.97 x 1024kg

Mass of the Moon = 7.35 x 1022kg

Mass of the Sun = 1.99 x 1030kg

Average Earth-Moon distance = 3.84 x 108m

Average Earth-Sun distance = 1.50 x 1011m

Answers

a) -7.62 x 1028 Joules

b) -5.28 x 1033 Joules

The planets orbit at different speeds.

• We can relate this to all the orbits of the planets around the sun.

• The closer the planet is to the Sun the faster its orbit, the greater its Kinetic Energy.

• The further away the slower the Kinetic Energy the greater the Potential Energy.

How fast do the planets orbit?

Planet Days to Orbit the Sun (0 d.p.)

Mercury 88

Venus 225

Earth 365

Mars 687

Jupiter 4333

Saturn 10759

Uranus 30685

Neptune 60190

Orbits of the inner planets

2. Many factors have to be taken into account to achieve a successful rocket launch,

maintain a stable orbit and return to earth.

Objects fall towards earth.

• At a given location on the earth and in the absence of air resistance, all objects fall with the same uniform acceleration. Thus, two objects of different sizes and weights, dropped from the same height, will hit the ground at the same time.

Information from http://thinkquest.org

Projectiles

• An object is controlled by two independent motions. So an object projected horizontally will reach the ground in the same time as an object dropped vertically. No matter how large the horizontal velocity is, the downward pull of gravity is always the same.

Information from http://thinkquest.org

Before Galileo

• This illustration reflects the general opinion before Galileo which followed largely Aristotelian lines but incorporating a later theory of "impetus" -- which maintained that an object shot from a cannon, for example, followed a straight line until it "lost its impetus," at which point it fell abruptly to the ground.

Galileo -Projectiles follow a curved path.

• Later it was realized that projectiles actually follow a curved path. Yet no one knew what that path was, until Galileo. There was yet another brilliant insight that led Galileo to his most astounding conclusion about projectile motion. First of all, he reasoned that a projectile is not only influenced by one motion, but by two. The motion that acts vertically is the force of gravity, and this pulls an object towards the earth at 9.8 meters per second. But while gravity is pulling the object down, the projectile is also moving forward, horizontally at the same time. And this horizontal motion is uniform and constant according to Galileo's principle of inertia.

HSC Physics looks at three types of Projectiles.

1. A projectile fired from the ground at a certain angle.

2. A projectile fired from a height horizontally.3. A projectile fired at an angle from a height.

We will only look at projectiles in two dimensions horizontally and vertically.

The following slides show what each looks like.

yx

Horizontally from a height

Horizontally from a height

At an angle from a height

u

Solving Problems for Projectile Motion

Projectile Motion -Handout

Projectiles – First Hand

• Projectiles in the Sporting Arena.

- Throwing a ball

• Computer Simulation

- Projectile Fired from the ground

Applet – Projectile Motion

Projectile Motion Problems

• Horizontal Problem– A coin is projected across a horizontal table with a constant

speed of 1.5m/s. It leaves the edge of the table and follows a parabolic path to the ground 1.0m below.

a) How long does it take to hit the ground?b) What is the vertical velocity just before the coin hits the

ground?c) Calculate the velocity just before it hits the floor?d) How far away from the edge of the table does the coin hit

the floor?

1.5m/s

Solution

A) All motion is in the same direction so we do not need to worry about vectors.

Uv=0m/s, a=9.8, sv=1.0m

Sv= uvt + ½ at2

1 = 0 + ½ (9.8)t2

t = 0.45 sec

So, the time of flight = 0.45 seconds

Solution

b) sv=1.0m, uv = 0, a = 9.8m/s2

Vv2 = uv2 + 2as

Vv2 = 0 + 2 x 9.8 x 1

Vv = 4.45 m/s

c) Velocity is Resultant of horizontal and vertical final velocity.

1.5 m/s

4.45m/s

A2 = b2 + c2A2 = (1.5)2 + (4.45)2

A = 4.67m/s

Angle = tan-1(1.5/4.45) = 18.7 degrees

Resultant Velocity = 4.67m/s at 18.7 degrees

Solution

d) Horizontal Displacement

Uh = 1.5m/s, t=0.45s

Sh = Uh x t

= 1.5 x 0.45s

= 0.675metres

1.5m/s

Important

Acceleration acts only on the vertical axis.

Therefore it does not affect any motion in the horizontal axis.

HomeworkAnswer the following questions:1. A spacecraft is rising from the moon with a velocity

of 20m/s when a bolt falls off. If the bolt takes 50.0s to reach the ground how high was the spacecraft?

2. On the planet Mars an astronaut throws a ball up at 10m/s.

a) How high does it go?b) How long does it take to reach this height?c) What is the time of flight?d) With what speed does it hit the ground?

3. During a visit to the Moon, an astronaut throws a rock vertically and it reaches a height of 20m.

a) With what speed was it thrown?b) How long did it take to reach 20m?c) At what times was the ball at 10m?

PROJECTILE MOTION LAB

• PURPOSE:To study projectile motion under a "real"

situation.

• PROCEDURE:Calibrate your ramp. Determine the velocity of

the ball as it leaves the ramp when rolled from different starting points along the ramp. Use the projectile motion of the ball onto the table top for your calculations. You should calibrate many points, at least every 2 cm or even every cm. Note the letter of your ramp.

After the ramp has been calibrated, it will be placed on a platform at a given height, H, and a cup will be placed on the floor at a given distance from the ramp, R. Your goal is to release the ball from the point your group decides along the ramp so that it will gain enough speed to just hit the cup.

SCORING:Hit on 1st try = 10 points Hit on 2nd try = 7 points Hit on 3rd try = 3 points

Newton’s Law of Universal Gravitation

• In simplistic terms, what Newton said was that an object attracts every other object in the universe. The two factors that determine the force of the attraction are:

- the mass of each of the two objects

- the distances between their centres of mass.• In mathematical terms, this is:

Click on EquationFor more information

Universal Gravitation

• F = force of attraction between objects• G = universal gravitational constant (which is

equal to 6.67 x 10-11 N m2 kg-2)• m1 = mass of object 1• m2 = mass of object 2• d = distance between their centres of mass

The observed solar system at the time of Newton

SunMercuryVenusEarthMarsJupiterSaturn

(all except Earth are named after Roman gods, because astrology was practiced in

ancient Rome)

Three outer planets discovered later…Uranus (1781, Wm Herschel)Neptune (1846 Adams; LeVerrier) Pluto (1930, Tombaugh)

To explain the motion of the planets, Newton developed three ideas:

1. The laws of motion2. The theory of universal gravitation3. Calculus, a new branch of mathematics

Newton solved the premier scientific problem of his time --- to explain the motion of the planets.

Isaac Newton

“If I have been able to see farther than others it is because I stood on the shoulders of giants.”

--- Newton’s letter to Robert Hooke,probably referring to Galileo and Kepler

m

Fa

221

r

mGmF

Uniform Circular Motion

Centripetalacceleration

Answer : 790 N

Example. Determine the string tension if a mass of 5 kg is whirled around your head on the end of a string of length 1 m with period of revolution 0.5 s.

For an object in circular motion, the centripetal acceleration is a = v 2/r . (Christian Huygens)

Uniform Circular Motion- Orbit of Satellites

• Forces involved in uniform circular motion – including satellites

• Kepler’s Laws

• Low Earth and geo-stationary orbits

• Orbital Decay of satellites

Forces and Uniform Circular Motion

• Objects do not perform uniform circular motion unless they are subject to a centripetal force. This is a force that is always perpendicular to the velocity of the object. That force causes the moving object to continually change direction so that it follows a circular path. The centripetal force is always directed toward the centre of the circular motion.

• The source of the centripetal force for a range of circular motions is listed here.  

Circular motion Source of centripetal force

Ball on a string whirled in a circle Tension in the string

Car driving around a corner Friction between the tyres and the road

Satellite orbiting the Earth Gravitational attraction between the Earth and the satellite

Three Ideas

• Centripetal Acceleration is the rate of change of velocity or speed of an object as it travels in circular motion. Measured in ms-2

• Centripetal Force is the force that pulls an object towards the middle of it’s circular motion. Gravity is the Centripetal force causing the motion of the planets.

• Centrifugal Force is the outwards push felt by an object as it undergoes circular motion. It is not a real force though.

•You may feel a force push you outwards when you are on a merry go round. All it is however is the Inertia of the body, because the motion is always accelerating in a circle. You want to keep travelling in a straight line but holding on to the pole forces you to stay on and accelerates you towards the middle of the circle.

Centripetal Force

• Using the idea of Centripetal Acceleration and Newton’s Second Law F = m.a we are able to calculate the Force involved in keeping an object in uniform circular motion.

r

mvF

2

F = Force Newtons

m = mass of object in kg

v = velocity in m/s

r = radius in m

Problem

• A 200kg satellite is orbiting Earth with a height of 250km. It’s orbital speed is 27 800km/h.

• Find the Force acting on it and its centripetal acceleration.

Height = 250km

Radius Earth = 6380km

Orbital Speed = 27800km/h

Solution

• Data

– M = 200kg

– V = 27800km/h

– R = 6380km + 250km

r

mvF

2

• Calculation

222

2

0.9200

1799

6630000

7722

Earth of centre the towards1799 So,6630000

7722200

msm

F

r

va

NF

F

cc

c

c

Newton and the Apple

Newton was inquisitive and it was why he was such a great scientist

Newton observed an apple and how gravity affected it on Earth. Some people say it hit him on the head and all of a sudden he knew how it worked.

He asked himself:

Did the same gravity go all the way to the moon?

Newton and the Moon

• Newton asked himself:What if the Moon was always falling towards Earth but never actually

got any closer? How could it do this?

The apple when it fell always fell to Earth.

What about if he threw the apple, what path did it take?

A curved path like the projectiles.

What if he threw the apple hard enough?

He thought possibly if he threw it hard enough it would continue to curve towards Earth but never actually land, in effect it became a moon.

Now he could escape Earth

So if he threw the apple hard enough it would leave Earth.

Could he throw an apple hard enough? No

What could he use?He thought of using a huge

cannon to fire a cannon ball fast enough that it may begin to orbit the Earth like the Moon did.

Applet for Newton’s Mountain Cannon http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/newt/newtmtn.html

Kepler’s Laws

More Information

Demonstrations of Kepler’s LawsDemonstrations of Kepler’s LawsKepler’s First and Second Laws

Kepler’s Third Law

Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.

1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.

2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.

3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.

Information from: http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html

"By the study of the orbit of Mars,we must either arrive at the secrets of astronomy or forever remain in ignorance of them."

- Johannes Kepler

Kepler’s 1st Law• The Law of Orbits

All planets move in elliptical orbits, with the sun at one focus.

The Elliptical shape of the orbit is due to the Inverse Square Law of Gravity.

That means the closer the planet gets to the sun the faster it will travel.

Kepler’s 2nd Law

• The Law of Areas

Kepler’s 3rd Law

• The Law of Periods– The way Kepler

showed it worked.3

2

22

31

21

r

T

r

T

We can use Earth’s orbit to calculate the mean radius of Mercury around the sun.

Data

Mean radius of Earth to Sun = 1.5 x1011 m

Period of Earth orbit = 3.16 x 107 s

Period of Mercury orbit = 88 Earth days

Kepler’s Law shows how it works for the entire Solar System

r3

t2

Kepler’s Laws Flashlet

• Have a go at creating your own orbits to look at Kepler’s Laws

http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/kepler6.htm

Newton proved Kepler’s Law of Periods with Gravitation

2

22

22

2

2

2

4

T

2 ,

T

2remember v

T

r

r

GM

rvSo

r

r

GMv

r

mv

r

MmGF

He used his Universal Gravitation and Circular Motion to solve it.

GMr

T 2

3

2 4

T= Period in sec

R = radius in metres

G = Gravitational Constant

M = Mass of Large object kg

Problem

• Determine the period of motion for a satellite orbiting a planet when– Planet’s mass is 7.2x 1012 kg– Mean dist. of satellite to planet is 3.0 x 104m

• For the same planet a moon has twice the period in comparison to the satellite.– What is the moon’s distance from the planet.

Calculating the Motion of Satellites

• Gravitation provides the centripetal force that produces the circular motion that is the satellite’s orbit around a planet. Therefore, it can be said that:

Gravitational force = Centripetal force

Satellite Motion Principles

Satellite Motion Mathematics

Types of OrbitsThe LEOs and the Geos• LEO or Low Earth Orbit is an orbit higher than

250km and lower than 1000km.• A Geostationary orbit is at an orbit where the

period of the Satellite’s orbit is equal to the Earth’s period of rotation. It is approximately an altitude of 35,800km.

Homework

• Find some uses for both Geos and Leos.

• What is the difference between a Geostationary and a Geosynchronous satellite?

Rocket Launch

Pioneers of Space Exploration

• Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O‘Neill and von Braun

• Library and Internet Lesson.

• Handout

• As a class we will gather information together and create a timeline showing the cause and effect of these physicists discoveries

Rocket Launch

• Escape Velocity

• G Force

• Effect of Earth’s orbital motion on the Rocket

• Changing Acceleration of Rocket in terms of:

- Law of Conservation of Momentum

- forces experienced by astronauts

Escape Velocity

Click here to calculate escape velocity on other planets

Handout on Escape Velocity

Calculating Escape Velocity

• To get something off Earth we need the Kinetic Energy to equal or overcome the Potential Energy that the Gravitational Field provides.

• Therefore the Law of Conservation of Energy means that

KE = PE

r

GMmmvesc 2

2

1M = mass of Earth

m = mass of object

V = velocity

R = distance from centre of Earth

Simplified Escape Velocity

r

GMvesc

2

So calculate how fast we need to go from Earth’s surface to escape Earth’s gravity.

Mass of Earth

= 5.98 x1024

Radius to Earth’s Surface

= 6.37 x106

Answer = 11.2 km/s

How would the rotation of Earth affect the launch of a rocket?

• As the Earth spins on its axis of course depending on where the rocket exits means it will be affected by he spin.

• Therefore if the rocket exits with the spin it gets a boost of speed.

• Yet if it exits against the spin of Earth it must travel even faster to gain the required speed to get where it wants to go.

It is easier to launch to the East.Earth's rotational velocity is 465 m/s to the east at the

equator.

Remember the Average Escape Velocity is 11.2km/s so,

A rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s relative to earth to escape

whereas

A rocket launched tangentially from the Earth's equator to the west requires an initial velocity of about 11.665 km/s relative to earth.

• If a rocket travels fast enough to escape Earth’s atmosphere and reduce the Gravitational pull it then enters the pull of the Sun.

• Therefore timing is also important for sending a rocket or probe for deep space missions. Why do you think?

What about the Sun and Earth’s orbit?

Acceleration of Rockets• As a rocket takes off it is acted upon by two forces.

– Gravity– Thrust from the engine

mgTweightthrustmaF

m

mgTa

To be able to accelerate upwards the rocket’s thrust must be greater than that of its weight.

So acceleration of a rocket is mathematically calculated by,

As the rocket goes upwards fuel is burnt and the mass of the rocket becomes smaller.The mass gets smaller so acceleration increases from Newton’s Second Law.

The Conservation of Momentum in Rocket Launch

• The rocket exhaust is what provides the thrust in the rocket launch. Gases are ejected from the back of the rocket and hence push the rocket in the opposite direction. Therefore the exhaust provides the impulse that drives the rocket upwards.

rocket

gasesrocket

rocketgases

rocketgases

m

mvv

mvmv

pp

)(

)()(

•Newton’s Third Law states for every action there is an equal and opposite reaction. So the change in momentum of the gases equals the change in momentum of the rocket only in the opposite direction.

Gravitational Acceleration

• Gravitational Acceleration Information

PioneersIdentify data sources, gather, analyse and present information on the contribution

of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O‘Neill or von Braun

• Some useful data sources on rocket pioneers that are available from the Internet are provided below. Decide on the type of information you will collect. Presenting information in chronological sequence would be appropriate.

The evolution of the rocket NASA Robert Goddard and his rockets NASA The beginning From Space exploration: from Talisman of the past to gateway for the future, John F. Graham, 1995, Chapter 7. Department of Space Studies, University of North Dakota, USA The pioneers of rocketry & space travel The ThinkQuest web site

Note that there are several other important rocket pioneers not mentioned in this syllabus point for which information is readily available. Conversely, not all of the pioneers mentioned have a plentiful supply of information available. Nevertheless, there is a great deal of information available on Tsiolkovsky and Goddard, in particular.

• Gather information from a range of sources. Analyse the information by identifying trends and relationships as well as contradictions in data and information.

• Select and use an appropriate media to present your data and information. The use of an annotated timeline would be appropriate.

Slingshot Effect or Gravity Assist

&Safe Re-entry to Earth

The slingshot effect is used to increase - or sometimes to decrease - the the speed, and to change the direction of motion of an interplanetary spacecraft.

The Slingshot Effect

SlingshotEffectSattEarth.mov

Three bodies must always be involved for the slingshot effect to operate.

The satellites (usually a planet and an artificial one) must both be in orbit around a third central body.

As a result of the slingshot effect, the satellite gains momentum relative to the central body.

The Slingshot Effect

SlingshotEffectSattEarth.mov

xx

The momentum gained by the satellite is not transferred back to the planet after the satellite-planet interaction.

The Slingshot Effect

SlingshotEffectSattEarth.mov

Momentum is transferred between the two because of the gravitational interaction between them.

To gain momentum the satellite must approach the planet so that it passes behind the planet in its orbit.

xx

The Slingshot Effect

xx

The slingshot effect

• The slingshot effect is also known as a planetary swing by or a gravity-assist manoeuvre. It is performed to achieve an increase in speed and/or a change of direction.

• A spacecraft is aimed close to a planet. As it approaches, the spacecraft is caught by the gravitational field of the planet, and swings around it. The speed acquired is then sufficient to throw the spacecraft back out again, away from the planet. By controlling the approach, the outcome of the manoeuvre can be manipulated.

The Slingshot Effect

Slingshot Effect

Momentum of a spacecraft cannot be increased if the

planet is stationary. All that can be achieved is a

change of direction.

Notice in the vector diagram the magnitude

does not change.

Image thanks to http://en.wikipedia.org/wiki/Gravitational_slingshot

Let’s see it in action

The Voyager Probes

Slingshot Effect

When a planet is moving a spacecraft can use the motion of the planet to

gain velocity. It does this by taking a very small amount of momentum away from the planet’s

motion.

Notice in the vector diagram the magnitude and direction changes.

Image thanks to http://en.wikipedia.org/wiki/Gravitational_slingshot

Slingshot Effect Flashlet

• http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/Slingshot.htm

Landing a Rocket

• Issues of safety for rocket re-entry into Earth’s atmosphere and landing on Earth’s surface

- Heat

- G-Forces

- Radio Blockout

- Landing

Re-entry of Shuttle

• Problems to overcome in Re-entry– Extreme Heat– G Forces– Communication problems

Homework

How do these problems impact on the shuttle’s travel?

What are some features of the shuttle that aim to reduces these impacts?

G Forces

• G-Forces  Gravity effects all objects within the Earth's gravitational

field - G-force.

When a person is standing still on the earth, they are experiencing One G (one times the force of gravity).

When a pilot in an airplane changes its orientation rapidly (tight turns, loops, etc.), the aircraft will undergo additional G-forces. These may be positive or negative G-forces.

Effects on Astronauts- G Forces

• G force is a ratio that compares an acceleration to the acceleration due to gravity. An acceleration of 9G means an astronaut will feel a force 9 times that of the pull of gravity.

• How much can a person withstand?– 8G is the maximum safe load– Ideally 3G is aimed for

Positive G Forces

• Positive G's are generated when an aircraft pitches upwards (the nose pulls up). For example, when the aircraft turns quickly or pulls up sharply. A World War II fighter may be capable of generating 7 G's or more. The physical effect of Positive G's on a pilot is a possible blackout.

• This is caused by the increased effort the heart must generate to counter the G-forces and still supply the brain with sufficient blood. When the G-forces are too great, the pilot will slowly lose vision due to this lack of blood supply. When prolonged, the blackout can cause a loss of consciousness.

Orbiting spacecraft have a large amount of energy due to their:

Issues affecting spacecraft re-entry and landing

• Altitude (giving the spacecraft potential energy)

• Speed (giving the spacecraft kinetic energy)

Problem: The space shuttle has a mass of approximately 82 tonnes when it begins its re-entry manoeuvres. At an altitude of 300 km, the shuttle has an orbital period of 91 minutes. Compare the kinetic and potential energies of the space shuttle at this altitude.

MEarth = 5.97x1024 kg note that:

REarth = 6378 km

Ep =

= 2.3x1011 JEk =

= 0.5 x 82000 x 77002 = 2.43 x 1012 J

6.67 10–11 5.97 1024 82000x1

6378000–

1

6678000

GMm

r

1

2mv2

v 2RT

Issues affecting spacecraft re-entry and landing

For a satellite in LEO, the kinetic energy is about ten times the potential energy and they are both very significant quantities of energy.

Issues affecting spacecraft re-entry and landing

To land safely, a spacecraft must reduce its speed by 90% as it approaches the Earth.

The speed reduction is accomplished through

• Retro-rocket firing (slows the vehicle by about 1%)

• Frictional drag in the atmosphere

Frictional drag through the Earth’s atmosphere converts the energy of the satellite to heat energy.

Issues affecting spacecraft re-entry and landing

For spacecraft intended to for return to Earth, dissipation of the heat energy generated by during re-entry is a major consideration in the spacecraft design and re-entry process.

Key strategies employed to ensure the spacecraft does not burn up include the use of• heat resistant (high melting point) materials

• materials with very low thermal conductivity

• materials with a very low heat capacity

• ablation (burning off of material from the craft)

• heat radiation from the heated surface of the spacecraft

Issues affecting spacecraft re-entry and landing

Retro-rockets slow the spacecraft slightly, causing its orbit to decay.

The lower orbit results in much greater frictional drag, greatly slowing the spacecraft.

The angle at which the spacecraft enters the atmosphere is critical.

• Too shallow an angle will cause the satellite to bounce off the atmosphere and re-enter space

• Too steep an angle will cause too great an increase in drag, causing the spacecraft to burn up in the atmosphere

Issues affecting spacecraft re-entry and landing

There is thus an optimum angle at which a spacecraft returning to Earth must enter the atmosphere

• 5–7°

Spacecraft - capsule

ablative heat shield

Spacecraft

space shuttleIf space science was like sport!

Protection of the shuttle during reentry is achieved by insulating tiles made of silica and placed on the under side of the craft.